Subgroups — C₂×D₃₁₀₄ #27144034

Order 12416.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₁₅₅₂	C₂	1	2	yes	maximal, complemented
2	D₃₁₀₄	C₂	1	4	yes	maximal, direct product factor
3	C₂×C₃₂×C₉₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×D₇₇₆	—	2	2	no	—
5	D₁₅₅₂	—	2	2	no	—
6	D₁₅₅₂	C₂²	1	4	yes	complemented
7	C₂×C₁₆×C₉₇	C₂²	1	1	yes	characteristic
8	C₃₂×C₉₇	C₂²	1	2	yes	complemented
9	C₂×D₃₈₈	—	4	2	no	—
10	D₇₇₆	—	2	4	no	—
11	D₇₇₆	—	4	2	no	—
12	C₂×C₈×C₉₇	D₄	1	1	yes	characteristic
13	C₁₆×C₉₇	D₄	1	1	yes	characteristic
14	C₁₆×C₉₇	C₂³	1	1	yes	characteristic
15	C₂²×D₉₇	—	8	2	no	—
16	C₂×C₄×C₉₇	D₈	1	1	yes	characteristic
17	D₃₈₈	—	4	4	no	—
18	D₃₈₈	—	8	2	no	—
19	C₈×C₉₇	D₈	1	1	yes	characteristic
20	C₈×C₉₇	C₂×D₄	1	1	yes	characteristic
21	C₂²×C₉₇	D₁₆	1	1	yes	characteristic
22	C₂×D₉₇	—	8	4	no	—
23	C₂×D₉₇	—	16	4	no	—
24	C₄×C₉₇	D₁₆	1	1	yes	characteristic
25	C₄×C₉₇	C₂×D₈	1	1	yes	characteristic
26	C₂×C₉₇	D₃₂	1	2	yes	complemented
27	C₂×C₉₇	C₂×D₁₆	1	1	yes	characteristic
28	D₉₇	—	16	4	no	—
29	C₂×D₃₂	—	97	1	no	maximal, Sylow
30	C₉₇	C₂×D₃₂	1	1	yes	characteristic, complemented, Sylow
31	C₂×D₁₆	—	97	2	no	—
32	D₃₂	—	97	4	no	—
33	C₂×C₃₂	D₉₇	1	1	yes	characteristic, complemented
34	C₂×D₈	—	194	2	no	—
35	D₁₆	—	97	4	no	—
36	D₁₆	—	194	2	no	—
37	C₂×C₁₆	C₂×D₉₇	1	1	yes	characteristic
38	C₃₂	C₂×D₉₇	1	2	yes	complemented
39	C₂×D₄	—	388	2	no	—
40	D₈	—	388	2	no	—
41	D₈	—	194	4	no	—
42	C₂×C₈	D₃₈₈	1	1	yes	characteristic
43	C₁₆	D₃₈₈	1	1	yes	characteristic
44	C₁₆	C₂²×D₉₇	1	1	yes	characteristic
45	C₂³	—	776	2	no	—
46	D₄	—	776	2	no	—
47	D₄	—	388	4	no	—
48	C₂×C₄	D₇₇₆	1	1	yes	characteristic
49	C₈	D₇₇₆	1	1	yes	characteristic
50	C₈	C₂×D₃₈₈	1	1	yes	characteristic
51	C₂²	—	776	4	no	—
52	C₂²	—	1552	4	no	—
53	C₂²	D₁₅₅₂	1	1	yes	characteristic
54	C₄	D₁₅₅₂	1	1	yes	characteristic
55	C₄	C₂×D₇₇₆	1	1	yes	characteristic
56	C₂	—	1552	4	no	—
57	C₂	D₃₁₀₄	1	2	yes	direct product factor
58	C₂	C₂×D₁₅₅₂	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₁₅₅₂
commutator, cosocle	C₁₆×C₉₇	C₂³
Frattini	C₁₆	C₂²×D₉₇
Fitting	C₂×C₃₂×C₉₇	C₂
socle	C₂²×C₉₇	D₁₆
hypercenter	C₂×C₃₂	D₉₇
hypocenter	C₉₇	C₂×D₃₂
LCS	G ▷ C₁₆×C₉₇ ▷ C₈×C₉₇ ▷ C₄×C₉₇ ▷ C₂×C₉₇ ▷ C₉₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ C₂×C₃₂

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₂×D₁₅₅₂	C₂	semidirect
2. D₃₁₀₄	C₂	direct (N × H)
3. C₂×C₃₂×C₉₇	C₂	semidirect
6. D₁₅₅₂	C₂²	semidirect
8. C₃₂×C₉₇	C₂²	semidirect
26. C₂×C₉₇	D₃₂	semidirect
30. C₉₇	C₂×D₃₂	semidirect
33. C₂×C₃₂	D₉₇	semidirect
38. C₃₂	C₂×D₉₇	semidirect
57. C₂	D₃₁₀₄	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×D₁₅₅₂	2
D₃₁₀₄	2
C₂×C₃₂×C₉₇	2
C₂×D₃₂	97

Subgroups — C2×D3104 #27144034

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×D₃₁₀₄ #27144034